Cesium-134 is a β emitter with a half-life of 2.0 years. How much of a 2.50-g sample of cesium-134 will remain after 10 years?
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after 10 years, the substance will undergo 5 half lives each of 2 years.
so matter left in first half life is 1/2* 2.50g = 1.25g
in second half life is 1/2* 1.25g = 0.625g
similarily for n half lives, 1/2 is multiplied n times, i.e. (1/2)^n to the initial total mass and we get the residual matter.
So for 5 half lives , left matter ={ (1/2)^5}*2.50 = 2.50/32 = 0.078125g
so matter left in first half life is 1/2* 2.50g = 1.25g
in second half life is 1/2* 1.25g = 0.625g
similarily for n half lives, 1/2 is multiplied n times, i.e. (1/2)^n to the initial total mass and we get the residual matter.
So for 5 half lives , left matter ={ (1/2)^5}*2.50 = 2.50/32 = 0.078125g
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